Characterization of nonlinear stress relaxation of the femoral and tibial trabecular bone for computational modeling

Computational models of orthopedic reconstructions are reliant on bone material properties, but viscoelastic behavior of trabecular bone is often ignored in numerical simulations. The inclusion of stress relaxation could be of importance for the accuracy of models simulating the primary stability of cementless implants. In this study, a material model to describe the nonlinear viscoelastic behavior of human trabecular bone was constructed based on uniaxial stress relaxation experiments. The relationship of bone mineral density (BMD) and stress relaxation was explored, and the material model was implemented in sample-specific finite element (FE) simulations.

Cylindrical trabecular human bone specimens, from the distal femur and proximal tibia, were subjected to stress relaxation tests, undergoing compression with strains from 0.2 % to 0.8 % for 30 min on four consecutive days. The experimental data were extrapolated to 24 h. Similar levels of stress relaxation were found for femoral and tibial specimens, with an average 54.4 % stress relaxation and a maximum level of 81.6 %. Using a modified superposition model, the specimen-specific nonlinear stress relaxation behavior was captured. However, when the samples were considered collectively, no correlation was found between applied strain, BMD and the viscoelastic response. Therefore, the average level of stress relaxation in combination with existing BMD-stiffness relationships were implemented in FE simulations for each individual specimen. While the FE models, on average, overestimated the overall stiffness by 64 %, they were able to adequately capture the stress relaxation response.